IFAC Professional Brief
Modelling of physical systems for the design and control of mechatronic systems

https://doi.org/10.1016/S1367-5788(03)00010-5Get rights and content

Abstract

Mechatronic design requires that a mechanical system and its control system be designed as an integrated system. This contribution covers the background and tools for modelling and simulation of physical systems and their controllers, with parameters that are directly related to the real-world system. The theory will be illustrated with examples of typical mechatronic systems such as servo systems and a mobile robot. Hands-on experience is realised by means of exercises with the 20-sim software package (a demo version is freely available on the Internet).

In mechatronics, where a controlled system has to be designed as a whole, it is advantageous that model structure and parameters are directly related to physical components. In addition, it is desired that (sub-)models be reusable. Common block-diagram- or equation-based simulation packages hardly support these features. The energy-based approach towards modelling of physical systems allows the construction of reusable and easily extendible models. This contribution starts with an overview of mechatronic design problems and the various ways to solve such problems. A few examples will be discussed that show the use of such a tool in various stages of the design. The examples include a typical mechatronic system with a flexible transmission and a mobile robot. The energy-based approach towards modelling is treated in some detail. This will give the reader sufficient insight in order to exercise it with the aid of modelling and simulation software (20-sim). Such a tool allows high level input of models in the form of iconic diagrams, equations, block diagrams or bond graphs and supports efficient symbolic and numerical analysis as well as simulation and visualisation. Components in various physical domains (e.g. mechanical or electrical) can easily be selected from a library and combined into a process that can be controlled by block-diagram-based (digital) controllers.

This contribution is based on object-oriented modelling: each object is determined by constitutive relations at the one hand and its interface, the power and signal ports to and from the outside world, at the other hand. Other realizations of an object may contain different or more detailed descriptions, but as long as the interface (number and type of ports) is identical, they can be exchanged in a straightforward manner. This allows top–down modelling as well as bottom–up modelling. Straightforward interconnection of (empty) submodels supports the actual decision process of modelling, not just model input and output manipulation. Empty submodel types may be filled with specific descriptions with various degrees of complexity (models can be polymorphic) to support evolutionary and iterative modelling and design approaches. Additionally, submodels may be constructed from other submodels in hierarchical structures.

An introduction to the design of controllers based on these models is also given. Modelling and controller design as well as the use of 20-sim may be exercised in hands-on experience assignments, available at the Internet (http://www.ce.utwente.nl/IFACBrief/). A demonstration copy of 20-sim that allows the reader to use the ideas presented in this contribution may be downloaded from the Internet (http://www.20sim.com).

Introduction

Mechatronic design deals with the integrated design of a mechanical system and its embedded control system. This definition implies that it is important, as far as possible, that the system be designed as a whole. This requires a systems approach to the design problem. Because in mechatronics the scope is limited to controlled mechanical systems, it will be possible to come up with more or less standard solutions. An important aspect of mechatronic systems is that the synergy realised by a clever combination of a mechanical system and its embedded control system leads to superior solutions and performances that could not be obtained by solutions in one domain. Because the embedded control system is often realised in software, the final system will be flexible with respect to the ability to be adjusted for varying tasks.

The interdisciplinary field of mechatronics requires tools that enable the simultaneous design of the different parts of the system. The most important disciplines playing a role in mechatronics are mechanical engineering, electrical engineering and software engineering. One of the ideas behind mechatronics is that functionality can be achieved either by solutions in the (physical) mechanical domain, or by information processing in electronics or software. This implies that models for mechatronic systems should be closely related to the physical components in the system. It also requires software that supports such an approach. In an early stage of the design, simple models are required to make some major design decisions. In a later stage (parts of the), models can be more detailed to investigate certain phenomena more in depth. The relation to physical parameters like inertia, compliance and friction is important in all stages of the design. Because specialists from various disciplines are involved in mechatronic design, it would be advantageous if each specialist would be able to see the performance of the system in his or her own domain. It should be possible to see the performance of the mechatronic system in multiple views. Typical views that are important in this respect are:

  • Physical models

  • Bond graphs

  • Control engineering models

    • Block diagrams

    • Bode plots

    • Nyquist plots

    • State space description

  • Time domain

  • Animation

  • C-code of the controller

Often modelling, simulation and identification is done for systems that already exist. The design of a controller has to be done for an already realised and given ‘process’. When we talk about design the system does not yet exist, there may be a lot unknown in the beginning, but there is also much more freedom to modify the system, not only the controller, but also the ‘process’, the mechanical construction itself.

In a typical design, the following phases can be distinguished. This is an iterative process and it may be necessary to go back to an earlier phase when problems arise in a later phase of the design process:

  • Phase 1: A concept is made of the system that has to be constructed and taking into account the tasks that have to be performed, the major components and their dominant dynamic behaviour are identified and modelled.

  • Phase 2: Controller concepts can be evaluated on this simple model. This requires that the model be available, e.g. as a transfer function, or a state space description.

  • Phase 3: When the evaluation is successful, the different components in the system can be selected and a more detailed model can be made. The controller designed in phase 2 can be evaluated with the more detailed model and controller and component selection can be changed.

  • Phase 4: When phase 3 has been successfully completed the mechanical system can be built and the controller can be realised electronically or in software. It is to be preferred that the translation from the controller tested in simulations is automatically transferred to, e.g. C-code, without manually coding; not only because of efficiency reasons, but especially to prevent coding errors.

This professional brief will address these issues. In the first part some representative examples of mechatronic design problems will be treated, showing how modelling and controller design are closely interacting during the design process of a mechatronic system. This part is written from the perspective of a control engineer. These cases will make clear that physical models are essential when besides the design of a controller also design of the mechanical part of the system is being considered. In the second part, port-based modelling of physical systems is introduced.

Physical system modelling provides insight, not only in the behaviour of systems that an engineer working on multidisciplinary problems wishes to design, build, troubleshoot or modify, but also in the behaviour of the environment of that system. A key aspect of the physical world around us is that ‘nature does not know domains’. In other words, all boundaries between disciplines are man-made, but highly influence the way humans interact with their environment. A key point each modeller should be aware of is that any property of a model that is a result of the modeller’s choice, should not affect the results of the model. Examples of modeller’s choices are:

  • Coordinates

  • Metric

  • Domain boundaries

  • System boundaries

  • Relevance of time and space scales

Several attempts to unified or systematic approaches of modelling have been launched in the past. In the upcoming era of the large-scale application of the steam-engine, the optimization of this multi-domain device (thermal, pneumatic, mechanical translation, mechanical rotation, etc.) created the need for the first attempt to a systems approach. This need for such a ‘mechathermics’ approach was then named thermodynamics. Although many will not recognise the current treatment of thermodynamics as the first systems theory, it certainly was aimed originally in trying to describe the behaviour of such a system independently of the involved domains. However, it required a paradigm shift or ‘scientific revolution’ in the sense of Kuhn (1962) due to the fact that the concept of entropy had to be introduced for reasons of consistency, i.e. to be able to properly ‘glue’ these domains together with the concept of a conserved quantity called energy. The rather abstract nature of the concept of entropy has caused that students have considered thermodynamics a difficult subject ever since, resulting in only a relatively limited number of engineers and scientists actively using the thermodynamic approach in modelling of behaviour.

Despite the fact that the first evidence of the use of feedback dates back to 200–100 b.c. when water clocks required the water level in a reservoir to be kept constant, followed by Drebbel’s thermostat and James Watt’s fly-ball governor, it was only in the late nineteen twenties that feedback was realised by means of electric signals (Harold Stephen Black’s 1927 famous patent that he wrote on a copy of the New York Times). At first, electronic feedback was used internally, to reduce distortion in electric amplifiers but later, especially during World War II, this concept was used in radar control and missile guidance. One might say that the multidomain approach to feedback was transferred to a signal approach in which the external power supply did not need to be part of the behavioural analysis. However, a more important paradigm shift was still to come, viz. the idea that the use of feedback allowed the construction of components, viz. operational amplifiers, with which basic mathematical operations could be mimicked, leading to analogue computers. This gave a new meaning to the terminology ‘analogue simulation’ that until then was conceived as mimicking behaviour by means of analogue circuits or mechanisms.

Just after World War II, due to the rapidly increasing demand for electric power, the USA was in great need for power, in particular hydropower, plants that should be able to deal with large and sometimes rapid fluctuations in the power grid. Obviously, the success of control theory (cybernetics) during World War II inspired many to apply control theory to the dynamic problems involved in electric power production. One such a civil engineer by the name of Henry Paynter (http://www.hankpaynter.com/) tried to use the early analogue computers that he invented together with James Philbrick, to simulate the dynamics of the power plants to be built (http://www.me.utexas.edu/∼lotario/paynter/paynterbio.html). He used the common description of block diagrams that display the computational structure of the differential and algebraic equations being used, as these mathematical operations were to be mapped directly on the basic components of the analogue computer. However, for reasons that will become clear in the course of this contribution (viz. related to the concept of computational causality) he ran into formulation problems. At the beginning of the fifties, he realised himself that the concept of a ‘port’ introduced in electrical circuit theory by Wheeler and Dettinger (1949) a few years earlier, should be extended to arbitrary power ports that can be applied domain-independently. Power ports include mechanical ports, hydraulic ports, thermal ports, electric ports, etc., i.e. everything Paynter needed for the description of the dynamic behaviour of power plants (http://www.hankpaynter.com/Bondgraphs.html).

In the following decade, after moving to the MIT mechanical engineering department, he designed an efficient notation based on the efficient representation of the relation between two ports by just one line that he called a ‘bond’. This so-called ‘bond graph’ notation was completed when he finally introduced the concept of the junction in 1959 (Paynter, 1961). Junctions not only make bond graph a powerful tool, but they are rather abstract concepts. Just like thermodynamics, bond graphs never became widely popular, although they spread over the whole world and are still alive after more than forty years. By contrast, signal processing, analogue and later digital computing, were not constrained to physical reality. This allowed people to mimic virtually everything, from physically correct or incorrect models to arbitrary mathematical relations that described imaginary systems. In the previous decennium, this even led to concepts like a ‘cyber world’, etc. even though the level of physical modelling in most virtual environments is rather low, as demonstrated by the unnatural features of much virtual behaviour.

Nevertheless, the introduction of rapid and flexible machinery for production, assembly, manipulation (including surgery), etc. that has truly taken off in the nineties, introducing again the need for a systems approach. In these application areas, physical constraints still limit imagination. The dynamics of such devices heavily leans on the application of digital electronics (microcomputers) and software. But a domain-independent description of the parts in which power plays a role is crucial to make a designer aware of the fact that a considerable part of these systems is constrained by the limits of the physical world. This mix of mechanics, or rather physical system engineering in general at the one hand and digital electronics, software and control at the other hand has been named ‘mechatronics’.

Obviously, a smooth connection is needed between the information-theoretical descriptions of the behaviour of digital systems and physical systems theory. From its introduction, bond graphs have allowed the use of signal ports, both in- and output, and a corresponding mix with block diagrams. As all digital operations can be successfully represented by block diagrams similar to mathematical operations, the common bond graph/block diagram representation is applicable. This graphical view supports a hierarchical organization of a model, supporting reusability of its parts.

However, many systems that are studied by (mechatronic) engineers differ from the engineering systems that were previously studied in the sense that the spatial description of complex geometries often plays an important role in the dynamic behaviour, thus including the control of these systems. This shows the need for a consistent aggregation of at the one hand the description of the configuration of a mechanism and at the other hand the displacements in a system that in some way are related to the storage of potential or elastic energy.

Another aspect of these systems is that only few realistic models can be solved analytically, emphasizing the important role of a numerical solution (simulation). The aggregation of numerical properties in the representation of dynamic systems allows that a proper trade-off is made between numerical and conceptual complexity of a model. The approach discussed herein offers a basis for making a trade-off between numerical and conceptual complexity, resulting in both a higher modelling efficiency and numerical simulation efficiency.

Motivated by the problems encountered in the examples, the energy-based approach towards modelling is treated in some detail necessary for the description of simple mechatronic systems. This will give the reader sufficient insight in order to exercise the approach with the aid of freely available demo version of the modelling and simulation software 20-sim. For more advanced issues the interested reader is referred to the references. The modelling and simulation tool 20-sim allows high level input of models in the form of iconic diagrams, equations, block diagrams or bond graphs and supports efficient symbolic and numerical analysis as well as simulation and visualisation. It is based on an approach to formulate mechanical constraints primarily in terms of velocities, not displacements. Basic elements and generic domain-dependent components in various physical domains (in particular the mechanical and electrical domain) can easily be selected from a library and combined into a process that can be controlled by block-diagram-based (digital) controllers as demonstrated in the case studies of the next sections.

Section snippets

Context

‘Mechatronic design deals with the integrated and optimal design of a mechanical system and its embedded control system’. This definition implies that the mechanical system is enhanced with electronic components in order to achieve a better performance, a more flexible system or just reduce the cost of the system. In many cases the electronics are present in the form of a computer-based embedded (control) system. This does not imply that every controlled mechanical system is a mechatronic

Modelling

During the design of mechatronic systems, it is important that changes in the construction and the controller be evaluated simultaneously. Although a proper controller enables building a cheaper construction, a badly designed mechanical system will never be able to give a good performance by adding a sophisticated controller. Therefore, it is important that during an early stage of the design a proper choice can be made with respect to the mechanical properties needed to achieve a good

Direct optimization of a physical variable

Suppose that the belt in the transmission has a limited strength. Using the state-event feature of 20-sim the moment of breaking of the belt can be exactly determined. This is shown in Fig. 33. Notice that because of the use of a physical model, the force signal is easily available.

Using a path generator can prevent excessive forces in the belt. In its basic form the path generator smoothes the reference step and filters out frequencies that excite the resonance frequencies. Further improvement

Design of a mobile robot

A typical example of the early design procedure is the conceptual design of a mobile assembly robot. Already in a very early stage of the design conflicting demands have to be resolved. Such a robot should be able to collect parts all around a production facility and do the assembly while driving. Because a high accuracy is required between the gripper of the robot and the surface where the parts are located, it is important that floor irregularities and vibration modes of the structure do not

Port-based modelling of dynamic systems

If modelling, design and simulation of (controlled) systems is to be discussed, some initial remarks at the meta-level are required. It should be clear and it probably is, due to the way it is phrased next, that no global methodology can exist that would deal with each problem that might emerge. In other words, no theory or model can be constructed independent of some problem context. Nevertheless, in practice, models are often considered as constructs that can be independently manipulated, for

Multiple view approach

It was already mentioned that commonly energy plays only a role in a part of a system. Furthermore, it is often fruitful to be able to look at all parts of a system from more than one point of view. This has been formalised as the so-called multiple view approach that is particularly well supported by window-based computer tools: a number of graphical representations like iconic diagrams (domain dependent), linear graphs (more or less domain-independent, but limited to the existence of analogue

Every model is wrong

This paradoxical statement seeks to emphasise that any model that perfectly represents all aspects of an original system is not a model, but an exact copy of that system (identity). When modelling one looks for simple but relevant analogies, not for complex identities. As a result, a model is much simpler than reality. This is its power and its weakness at the same time. The weakness is that its validity is constrained to the problem context it was constructed in, whereas its strength is the

Use of ports in dynamic system models

The concept of a port is generated by the fact that submodels in a model have to interact with each other by definition and accordingly need some form of interface. In physical systems, such an interaction is always (assumed to be) coupled to an exchange of energy, i.e. a power. In domain-independent terminology, such a relation is called a power bond accordingly. This bilateral relation or bond connects two (power) ports of the elements or submodels that are interacting (Fig. 41).

In the signal

Computational causality

Purely mathematically speaking one can state that a subsystem with a number of ports, called multiport, is a multiple-input–multiple-output or MIMO system, of which the set of inputs and the set of outputs is not a priori chosen. The relation between the input and output variables, the so-called constitutive relation, determines the nature of the multiport. If the number of input variables is not equal to the number of output variables, this means that there has to be at least one unilateral

Example of the use of the port concept

Only the actual use of the port concept can fully clarify its importance. Therefore, a simple example is discussed to illustrate the port concept.

A component that may be used in mechatronic systems, but in which the control is not realised by (digital) electronic signal processing, but physically, i.e. as an energetic process, is taken as an example. This choice is made in order to focus on the multidisciplinary modelling part on the basis of power ports. In the second part, the examples will

System versus environment: system boundary

The distinction between system and environment is determined by the role of these parts: the environment can influence the system, but not dynamically interact with it. In signal terminology: the environment may influence the system via inputs and observe the system via outputs, but the inputs cannot depend on these outputs, at least not at the time scale that is of interest. In case of normal use, a car battery, for example, may be considered the environment of a dashboard signal light, as the

Elementary behaviours and basic concepts

This section introduces the conceptual elementary behaviours that can be distinguished in the common description of the behaviour of physical systems, in particular from a port-based point of view. Before the individual elements are discussed, first the notation for the positive orientation in the form of the so-called half-arrow is introduced.

Causal port properties

Each of the nine basic elements (C, I, R(S), TF, GY, Se, Sf, 0, 1) introduced above has its own causal port properties, that can be categorised as follows: fixed causality, preferred causality, arbitrary causality and causal constraints. The meaning of these categories will become clear when the basic elements are discussed. For reasons of clarity, the sources are discussed first, after introduction of the notation by means of the so-called causal stroke (Karnopp & Rosenberg, 1975).

Causal analysis: feedback on modelling decisions

Causal analysis, also called causality assignment or causal augmentation, is the algorithmic process of putting the causal strokes at the bonds on the basis of the causal port properties induced by the nature of the constitutive relations.

Conclusion

In this professional brief, it has been shown how modern object-oriented modelling of physical systems can help to make proper decisions during the design of mechatronic systems. In the cases it has been demonstrated that this approach enables to easily change from finding solutions in the controller domain or in the mechanical structure itself. Software tools that cover the different domains support this process.

This second part emphasised the background of physical modelling in general. It

Job van Amerongen studied Electrical Engineering at Delft University of Technology where he obtained an M.Sc. degree in 1971 and a Ph.D. degree in 1982. From 1971 to 1973 he did his military service as an officer in the Royal Netherlands Navy. From 1973 to 1987 he was assistant and associate professor at the Control Laboratory of the Faculty of Electrical Engineering of Delft University of Technology, where he worked on applications of modern control theory, especially model reference adaptive

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    Job van Amerongen studied Electrical Engineering at Delft University of Technology where he obtained an M.Sc. degree in 1971 and a Ph.D. degree in 1982. From 1971 to 1973 he did his military service as an officer in the Royal Netherlands Navy. From 1973 to 1987 he was assistant and associate professor at the Control Laboratory of the Faculty of Electrical Engineering of Delft University of Technology, where he worked on applications of modern control theory, especially model reference adaptive control, in ship control systems and electrical power production systems.

    Since 1987, he is professor in Control Engineering in the Faculty of Electrical Engineering at the University of Twente. His current research interests are applications of modern control theory, especially intelligent control, in mechatronic systems. As head of the control laboratory he is also involved in the research in modelling and simulation of dynamical systems and in embedded control systems. He is scientific director of the Drebbel Institute for Mechatronics, of the University of Twente. He is member of the IFAC Technical Committee on Mechatronics and the IFAC TC on Marine Systems. From 1994 to 1998, he was dean of the Faculty of Electrical Engineering. In the first half year of 1999, he was on leave at the University of Newcastle in Australia.

    He is (co-) author of many papers on adaptive and intelligent control systems, mechatronics and automatic steering of ships, co-author of a book on adaptive control systems and author of three courses on systems and control of the Dutch Open University (http://www.ce.utwente.nl/amn).

    Peter Breedveld is an associate professor with tenure at the University of Twente, The Netherlands, where he received a B.Sc. in 1976, an M.Sc. in 1979 and a Ph.D. in 1984. He has been a visiting professor at the University of Texas at Austin in 1985 and at the Massachusetts Institute of Technology in 1992–1993 teaching integrated physical system modelling and dynamic systems and control. He is or has been an industrial consultant. He initiated the development of the modelling and simulation tool that is now commercially available under the name 20-sim. In 1990, he received a Ford Research grant (the first in continental Europe outside of Germany) for his work in the area of physical system modelling and the design of computer aids for this purpose.

    He is an associate editor of the ‘Journal of the Franklin Institute’, SCSSimulation’ and ‘Mathematical and Computer Modelling of Dynamical Systems’. His scientific interests are: integrated modelling, control and design of physical systems; graphical model representations (bond graphs); generalised thermodynamics; computer-aided modelling, simulation, analysis and design; dynamics of spatial mechanisms; mechatronics; generalised networks; numerical methods; applied fluid mechanics; applied electromagnetism; qualitative physics; surface acoustic waves in piezo-electric sensors and actuators.

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